On 6/9/23 12:52, Mathieu wrote:
The fact that f^h is no longer separated changes the solution of my pde
drastically:
If I run my program with the analytical f or with f^h on the axis parallel
grid, the output is quite similar. This is not so if I run it with f^h defined
on the rotated grid.
And since the axis parallel grid is able to capture the separation,
I hoped the rotated grid can capture it too.
But if I understood you correctly, there is no obvious workaround for this
issue , right?
When you discretize a function via interpolation of projection, you generally
lose most structural properties of the function -- for example, it will have a
different mean value, it may lose symmetry if your mesh is not symmetric, it
will only be in H^1 even though the original function may have been in
C^infty, and vector functions may no longer be divergence free after
projection. Some of these issues can be addressed by using specialized
operations (e.g., divergence free projections), but you generally have to
expect that whatever special property your original function has, the
interpolated or projected function will not any longer possess.
That happens to be one of the many things you just have to live with when
working with discrete functions.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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